853
A publication of
CHEMICAL ENGINEERING TRANSACTIONS
VOL. 31, 2013
The Italian Association
of Chemical Engineering
Online at: www.aidic.it/cet
Guest Editors: Eddy De Rademaeker, Bruno Fabiano, Simberto Senni Buratti
Copyright © 2013, AIDIC Servizi S.r.l.,
ISBN 978-88-95608-22-8; ISSN 1974-9791
Mass Burning Rate of a Large TBPB Pool Fire –
Experimental Study and Modeling
Stefan Schälikea,b, *, Kirty B. Mishraa, Marcus Malowa, Anka Bergera, KlausDieter Wehrstedta, Axel Schönbucherb
a
Federal Institute for Material Research and Testing (BAM), Unter den Eichen 87, 12205 Berlin, Germany
University Duisburg-Essen, Institute for Chemical Engineering I, Universitätsstr. 7, 45141 Essen, Germany
stefan.schaelike@bam.de
b
Data and prediction for the mass burning rate of a tert-butyl-peroxy-benzoat (TBPB) pool fire (pool
diameter = 3 m) is presented. The mass burning rates of TBPB fires are up to six times higher and less
dependent on pool diameter compared to hydrocarbon pool fires caused by an additional heat release rate
due to exothermic decomposition reaction in the liquid phase. This heat release rate is calculated using a
st
1 order reaction kinetic obtained from micro calorimetric measurements. A new model is derived
considering the heat release rate due to the decomposition reaction which is shown to be 100 % of the
heat release rate radiated to the pool surface. With the presented model, including also physical quantities,
especially the limiting fuel concentration for upward flame propagation, it is possible to predict the mass
burning rates of large TBPB pool fires. The predicted values are in very good agreement with the
experiments.
1. Introduction
Pool fires belong to the most frequent accidents when combustible substances are released in the process
industries during transport, handling or storage (Person and Lönnermark, 2004; Mannan, 2005). A pool fire
is defined as a buoyancy controlled non-premixed flame which burns above a liquid pool due to
vaporization with a small initial momentum. A key quantity for hazard calculations relating to pool fires in
fire safety science is the mass burning rate m
fcc . For hydrocarbon pool fires a wide set of experimental
data e.g. (Blinov and Khudiakov, 1957; Burgess et al., 1961; Mudan, 1984) and theoretical studies e.g.
(Hottel, 1959; Hertzberg, 1973; Burgess and Hertzberg, 1974) on the mass burning rates depending on
the fuel and pool diameter d are available. The mass burning rates of other hazardous substances like
organic peroxides are less understood and only a few sets of pool fire data are available (Wehrstedt and
Wandrey, 1993; Chun, 2005; Mishra and Wehrstedt, 2012). Di-tert-butyl-peroxy-benzoate (TBPB) is a
compound of wide industrial use as an initiator for radical reactions, a resin hardener or a cross linking
agent. To close the lack of missing data on the mass burning rates of organic peroxides a large-scale pool
fire experiment with TBPB is conducted. A new model to describe the mass burning rates of TBPB pool
fires taking into account the heat release rate due to the liquid phase decomposition reaction is presented.
2. Experimental setup
The large-scale experiment with the TBPB fire (d = 3 m) has been carried out on the open air BAM Testsite Technical Safety (in Horstwalde, south of Berlin). Steel trays were used with a rim height of 0.08 m,
the fuel layer had a thickness of 0.05 m. The mass loss during the burning of the fuel was measured with a
load cell mounted under the tray as one point of a three-point construction. The mass loss records had a
time resolution of 't = 0.1 s and a precision of 0.25 %. The fuel temperatures during the burning of the
peroxide were measured with NiCr-Ni thermocouples (1 mm in diameter, time resolution of 't = 0.01 s with
a precision of 0.1 K) connected to a multi data recorder. The thermocouples were placed in 1 cm steps on
the radial coordinate r beginning at the flame axis (r = 0) and on three axial positions xtc. The thermocouple
854
measurements are corrected for thermal conduction (Sears, 1954) against what heat losses due to thermal
radiation are negligible. The heat of combustion is measured with an IKA-C5003 using DIN 51900-3 (DIN
51900-3, 2005).
3. Theory
The experimental studies of Blinov and Khudiakov (1957) on liquid hydrocarbon (HC) pool fires have
shown two basic burning regimes are possible: convectively dominated burning for small diameter
d ” 20 cm and radiatively dominated burning for d • 20 cm, particularly for d • 1 m. In the convective
regime the flow can be laminar or turbulent and is always turbulent for radiatively driven flames. Flames in
the radiative regime can be optically thin or thick. These distinctions can be made on basis of the pool
diameter (Babrauskas, 1984) shown in Table 1.
Table 1: Burning modes of pool fires depending d
pool diameter d [m]
< 0.05
0.05 to 0.2
0.2 to 1
”1
burning mode
convective, laminar
convective, turbulent
radiative, optically thin
radiative, optically thick
For the mass burning rate Hottel (1959) has modelled:
Q
ba,tot (d )
m fcc (d )
where
(1)
AP (Tf,bp c p,v Tf,a cp,a 'hv )
is the total heat release rate back to the fuel surface, AP is the pool area, Tf,bp , Tf,a are the
Q
ba,tot
fuel temperatures at the boiling point (bp) and at ambient temperature (a), c p, v , c p,a are the heat capacities
of the fuel vapor and the liquid fuel at ambient temperature and 'hv is the enthalpy of evaporation. For
safety engineering application the radiative, optically thick regime is of primarily interest, so Eq.(1) can be
simplified to:
m fcc
where
Q
ba,rad
(2)
AP (Tf,bp cp,v Tf,a cp,a 'hv )
is the heat release rate due to radiation back to the fuel surface. For this radiation regime
Q
ba,rad
Burgess and Hertzberg (1974) developed a model based on the following physical quantities, where it is
assumed that the term with the heat capacity difference in the denominator of Eq. (2) is much smaller then
'hv :
m fcc { E
where
'hc
'hv
E
f rad
H F ,f
'hc
'hc
| 10 3
M F ,f c f S u
'hv
'hv
HF
(3)
is a composite factor, f rad is the fraction energy radiated, H F is the flame emissivity, H F,f is the
flame emissivity as viewed by the absorbing liquid fuel reservoir, M F,f is the view factor between the flame
and the fuel surface, cf
upper explosion limit,
UEL U v is the limit fuel concentration for upper flame propagation, UEL is the
U F is the density of the fuel vapor and S u is the limit burning velocity for natural
convection. For hydrocarbon pool fires realistic values for the quantities in E are f rad
M F,f = 0.4 , c f
0.032 ˜ 3 kg/m³ = 0.096 kg/m³ , Su = 0.06 m/s.
0.5 , H F / H F,f
0 .5 ,
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4. Results and discussion
4.1 Fuel surface temperature and heat of combustion
A measurement of the fuel surface temperatures is shown in Figure 1. The arrow indicates the time where
the fuel surface has the same height as the thermocouple. Hence, the fuel temperature of the liquid phase
is given on the left side of the arrow while the right side of the arrow shows the gas phase temperature
short above the fuel surface. An averaged value of the fuel surface temperature T v = 403 K is constant
over the surface area. The depth of penetration of the hot-zone a hz into the liquid fuel indicated by a
temperature increase to 310 K is much lower for TBPB pool fires ( a hz ,TBPB | 4.5 mm at t = 100 s) in
comparison to hydrocarbon pool fires e.g. n-heptane pool fires ( a hz ,HC | 12 mm at t = 100 s) (Nakakuki,
1994; Cheng et al., 2011). The smaller a hz ,HC is caused by the higher energy loss due to the high
evaporation rates in TBPB pool fires which inhibits the heat being conducted deep into the fuel. The sharp
temperature decrease at t = 130 s is due to the effect of a periodic flame oscillation which is not
considered in this paper (Mishra, 2009).
Figure 1: Fuel surface temperatures of a TBPB pool fire at the pool center, where xtc is the height of the
thermocouples over the pool surface
The measured heat of combustion is 'hc = 30,113 kJ/kg.
4.2 Mass burning rate
The mass burning rate of the TBPB pool fire (d = 3 m) during the steady burning time is measured to be
m cfc 0.37 kg/(m² s). It can be seen that the mass burning rate of the TBPB pool fire is up to six times
higher than mass burning rates known from hydrocarbon pool fires m
cfc ,TBPB (d
3 m) / m cfc , HC (d
3 m) | 6 .
In the following it can be shown that Eqs.(1-3) are not applicable for TBPB pool fires without modifications.
due to the decomposition reaction of the liquid TBPB which has
This is caused by a heat release rate Q
d
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to be introduced into Eqs. (1-3). Using the energy balance of Burgess and Hertzberg (1974) modified by
, leads to:
including the additional heat release rate Q
d
Q
ba,rad Q d
m fcc
(4)
AP (Tv cp,v Tf,a cp,a 'hv )
Eq. (4) is valid for radiatively controlled pool fires (d • 1 m) which occur during an accident and show a little
variation of the mass burning rate with increasing diameter. Therefore it is only necessary to predict one
critical value for the mass burning rate in a range d • 1 m.
in Eq.(4) can be calculated using the model assumption of an ideal, isotherm,
The heat release rate Q
d
continuous stirred tank reactor (CSTR). This model can be used, because the decomposition reaction
occurs only in a thin liquid layer. During the combustion process this layer sinks down, whereby the
products formed in the liquid phase by the decomposition reaction are vaporized and fresh liquid TBPB
enters into the reaction zone. The expected conversion is very small, so that the liquid is ideal mixed. The
thickness G rz of the reaction zone for a TBPB pool fire d = 3 m can be calculated using Eq.(5):
G rz
v a ( d ) W ( d ) | 3.6 ˜10 4 m/s ˜ 9 s | 3 ˜10 3 m
where v a
(5)
m fcc / U l is the burning velocity, W is the residence time and equal that time the liquid phase has a
temperature at which a significant conversion can occur (365 K < T < 403 K). A 1st order (n = 1) reaction
kinetic with a reaction rate constant k 9.5 ˜10 3 s-1 at T v = 403 K is taken from measurements of ChungPing et al. (2012). For the CSTR a residence time can be calculated by:
W (d )
Vrz
V
in
where Vrz
G rz
(6)
va ( d )
G rz AP is the volume of the reaction zone, Vin
va (d ) AP is the volume flow rate entering the
reaction zone. With known W and with a stoichiometric coefficient
be calculated by:
Q
1 the Damköhler number Da can
Da W k
(7)
The Damköhler number is directly connected to the conversion U in a CSTR for n = 1:
U
Da
1 Da
(8)
With the enthalpy of the exothermic decomposition 'hd = 1,377 kJ/kg obtained from measurements of
can be calculated as:
Malow and Wehrstedt (2005) the heat release rate Q
d
(m cc ) U (m cc ) m cc A ('h )
Q
d
f
f
f
P
d
(9)
Using Eqs. (4-9) and the heat capacities for TBPB cp,v = 1.4 kJ/(kg K) (Goos and Burcat, 2010),
cp,a = 1.7 kJ/(kg K) obtained from Gimzenski and Audley (1993), the enthalpy of vaporization 'hv = 205
kJ/kg (Lide, 1996), the heat release rate
for the radiative optical thick regime and the heat
Q
ba,rad,TBPB
can be calculated for the TBPB pool fire (Table 2). It can be recognized that the heat
release rate Q
d
. The fire is controlled by two different mechanism given by the
Q
ba,rad,TBPB
. The heat release rate Q
and the heat release rate Q
is about two
is § 100 % of
release rate Q
d
heat release rate
Q
ba,rad,TBPB
d
ba,rad,TBPB
times higher than those of hydrocarbon pool fires. The exothermic decomposition reaction plays a major
role in peroxide pool fires directly affecting the fuel surface area.
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Table 2: Heat fluxes of a radiatively controlled TBPB pool fire (d = 3 m)
Q
ba,rad,TBPB
Q
d
364 kW
366 kW
/Q
Q
d
ba,rad,TBPB
0.99
Q
ba,rad,HC
Q
ba,rad,TBPB / Q ba,rad,HC
190 kW
1.93
/A
Q
d
P
51 kW/m²
Based on Eqs. (3),(4),(9) a new model for m
fcc for TBPB pool fires is developed and leads in the radiatively
controlled limit (d • 1 m) to:
m fcc
§ E
·
1¸¸ Q
d / AP
© S u cf
¹
c p, v Tv c p,a Ta 'hv
E ('hc ) ¨¨
(10)
For the calculation of E from the quantities given in Eq.(3) the values of HC pool fires are used, but the fuel
concentration
cf is calculated using specific data for TBPB. This peroxide is flammable over a wide range
of mixtures up to < 100 % (Brandes and Möller, 2008). High concentrations of ignited TBPB do not yield in
carbon dioxide and water as main products. New investigations (Schälike et al., 2012) show that organic
peroxides have two different ignition steps in the fuel rich region. The first ignition step happens as a
thermal decomposition of the TBPB which leads in the gas phase mainly to the products benzene, carbon
dioxide, acetone and ethane (Tobolski and Mesrobian, 1954). The second ignition step is a high
temperature ignition of the decomposition products leading to chain branching. Hence, for flame
propagation not only the decomposition, but also the high temperature ignition has to be taking into
account. Therefore, the benzene concentration at
T v = 403 K is chosen as the limiting species for a
sustainable flame. Using the ideal gas law for density calculation U v and the upper explosion limit UEL
(8.6 vol.%, (Brandes and Thedeus, 2003)) of benzene leads to a limit benzene concentration of
cf = 0.086 ·2.4 kg/m³ = 0.21 kg/m³. With this value of cf for TBPB pool fires the constant E is calculated
as E = 1.32 ˜ 10 3 kg/(m² s). With the new model Eq. (10) it is for the first time possible to predict the mass
burning rates for large pool fires of liquid peroxides, e.g. TBPB or DTBP. Substituting the discussed values
for the influencing quantities into Eq.(10) a mass burning rate m
fcc, pred = 0.39 kg/(m² s) for a TBPB pool
fire (d = 3 m) in the radiatively controlled limit can be predicted in very good agreement with
measurements m
fcc,exp = 0.37 kg/(m² s). This model can be used to describe the mass burning rates of
large TBPB pool fires which is very helpful in safety science applications. For safety science it is also
important to have conservative values from the model which should not under predict the experimental
results.
5. Conclusions
In this study the mass burning rate of a TBPB pool fire is studied and a new model is developed. The
major results can be summarized:
1. The mass burning rate of a TBPB pool fire in the radiatively controlled optically thick regime is six times
higher than those of hydrocarbon pool fires.
due to an exothermic decomposition reaction in
2. For a TBPB pool fire an additional heat release rate Q
d
is based on a 1st order reaction kinetic
the liquid phase of the fuel is introduced. The calculation of Q
d
which depends on the conversion, mass burning rate, pool cross section, and the heat of decomposition.
is § 100 % of the heat release rate
It can be shown that Q
d
radiated back to the fuel surface.
Q
ba,rad,TBPB
a new model is developed to predict the mass burning rates for large pool
With the heat release rate Q
d
fires of liquid peroxides.
3. Further can be shown from the new model that the radiated heat release rate to the fuel surface of
TBPB pool fires is two times larger than that heat release rate for hydrocarbon pool fires.
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